What's the baseline here - in a world where every person is betting randomly X times a month, what would the distribution look like? There'd still be a small percentage that wins most of it, right?

We don't know the exact benchmark, but your insight is correct. We provide a simulation similar to what you have in mind towards the end of the paper, but you can generate almost any distribution you want by fine-tuning a simulation...

To relate it to a more-general economic article that has stuck with me for a while:

> If you simulate this economy, a variant of the yard sale model, you will get a remarkable result: after a large number of transactions, one agent ends up as an “oligarch” holding practically all the wealth of the economy, and the other 999 end up with virtually nothing.

https://www.scientificamerican.com/article/is-inequality-ine...